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On Estimating the Expected Rate of Return in Diffusion Price Models with Application to Estimating the Expected Return on the Market

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  • Goldenberg, David H.
  • Schmidt, Raymond J.

Abstract

This paper derives and numerically simulates maximum likelihood estimators for the drift in several important diffusion price models. The time series convergence properties of these estimators are compared to those of standard estimators including the geometric and arithmetic means. Merton (1980) demonstrated that it is difficult to efficiently estimate the drift in a log-normal diffusion model. We qualify and strengthen his result by noting that his estimator is the maximum likelihood estimator and by applying our simulation results. However, we also demonstrate that it is possible to efficiently estimate the drift in other useful diffusion price models. In particular, by asking just how much time is needed in order for the maximum likelihood estimators of the drift in different diffusion processes to converge, these results qualify and quantify Black's (1993) statement that “we need such a long period to estimate the average that we have little hope of seeing changes in expected return."

Suggested Citation

  • Goldenberg, David H. & Schmidt, Raymond J., 1996. "On Estimating the Expected Rate of Return in Diffusion Price Models with Application to Estimating the Expected Return on the Market," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(4), pages 605-631, December.
    • Handle: RePEc:cup:jfinqa:v:31:y:1996:i:04:p:605-631_02
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    Cited by:

    1. Yue Fang, 2000. "When Should Time be Continuous? Volatility Modeling and Estimation of High-Frequency Data," Econometric Society World Congress 2000 Contributed Papers 0843, Econometric Society.
    2. Braselton, James & Rafter, John & Humphrey, Patricia & Abell, Martha, 1999. "Randomly walking through Wall Street," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 49(4), pages 297-318.
    3. Basso, A. & Pianca, P., 1999. "A more informative estimation procedure for the parameters of a diffusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 45-53.

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